Data sets can frequently be partitioned into meaningful groups based on the variables they contain. Making this grouping explicit allows the computation of numeric summaries within groups, which in turn facilitates quantitative comparisons.

This is the second module in the Visualization and EDA topic.

Overview

Learning Objectives

Conduct exploratory analyses using dplyr verbs (group_by and summarize), along with numeric data summaries.

Video Lecture

Example

We’ll continue in the same Git repo / R project that we used for visualization, and use essentially the same weather_df dataset – the only exception is the addition of month variable, created using lubridate::floor_date().

weather_df = 
  rnoaa::meteo_pull_monitors(
    c("USW00094728", "USW00022534", "USS0023B17S"),
    var = c("PRCP", "TMIN", "TMAX"), 
    date_min = "2021-01-01",
    date_max = "2022-12-31") |>
  mutate(
    name = recode(
      id, 
      USW00094728 = "CentralPark_NY", 
      USW00022534 = "Molokai_HI",
      USS0023B17S = "Waterhole_WA"),
    tmin = tmin / 10,
    tmax = tmax / 10,
    month = lubridate::floor_date(date, unit = "month")) |>
  select(name, id, everything())

Initial numeric explorations

Before beginning to summarize data, it can help to use initial visualizations to motivate some data checks or observations. Consider, for example, this histogram of precipitation values:

weather_df |> 
  ggplot(aes(x = prcp)) + 
  geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Warning: Removed 15 rows containing non-finite values (`stat_bin()`).

This is clearly a very skewed distribution; any formal analyses involving preciptation as a predictor or outcome might be influenced by this fact. It’s important to note that the vast majority of days have no precipitation. Meanwhile, examining the relatively few days have very high precipitation might be helpful.

weather_df |> 
  filter(prcp >= 1000)
## # A tibble: 3 × 7
##   name           id          date        prcp  tmax  tmin month     
##   <chr>          <chr>       <date>     <dbl> <dbl> <dbl> <date>    
## 1 CentralPark_NY USW00094728 2021-08-21  1130  27.8  22.8 2021-08-01
## 2 CentralPark_NY USW00094728 2021-09-01  1811  25.6  17.2 2021-09-01
## 3 Molokai_HI     USW00022534 2022-12-18  1120  23.3  18.9 2022-12-01

The two high rainfall days in NYC correspond to tropical storm Henri and hurricane Ida, while the high precipitation day in Molokai took place during a notable cold front.

A close look at the scatterplot below (which focuses on a range of values to emphasize this point) suggests that Central Park and Molokai report temperature values differently from Waterhole …

weather_df |> 
  filter(tmax >= 20, tmax <= 30) |> 
  ggplot(aes(x = tmin, y = tmax, color = name, shape = name)) + 
  geom_point(alpha = .75)

Depending on the nature of later analyses, understanding how these differ and implementing an approach to bring the reports into alignment might be necessary.

group_by

Datasets are often comprised of groups defined by one or more (categorical) variable; group_by() makes these groupings explicit so that they can be included in subsequent operations. For example, we might group weather_df by name and month:

weather_df |>
  group_by(name, month)
## # A tibble: 2,190 × 7
## # Groups:   name, month [72]
##   name           id          date        prcp  tmax  tmin month     
##   <chr>          <chr>       <date>     <dbl> <dbl> <dbl> <date>    
## 1 CentralPark_NY USW00094728 2021-01-01   157   4.4   0.6 2021-01-01
## 2 CentralPark_NY USW00094728 2021-01-02    13  10.6   2.2 2021-01-01
## 3 CentralPark_NY USW00094728 2021-01-03    56   3.3   1.1 2021-01-01
## 4 CentralPark_NY USW00094728 2021-01-04     5   6.1   1.7 2021-01-01
## 5 CentralPark_NY USW00094728 2021-01-05     0   5.6   2.2 2021-01-01
## 6 CentralPark_NY USW00094728 2021-01-06     0   5     1.1 2021-01-01
## # ℹ 2,184 more rows

Several important functions respect grouping structures. You will frequently use summarize to create one-number summaries within each group, or use mutate to define variables within groups. The rest of this example shows these functions in action.

Because these (and other) functions will use grouping information if it exists, it is sometimes necessary to remove groups using ungroup().

Counting things

As an intro to summarize, let’s count the number of observations in each month in the complete weather_df dataset.

weather_df |>
  group_by(month) |>
  summarize(n_obs = n())
## # A tibble: 24 × 2
##   month      n_obs
##   <date>     <int>
## 1 2021-01-01    93
## 2 2021-02-01    84
## 3 2021-03-01    93
## 4 2021-04-01    90
## 5 2021-05-01    93
## 6 2021-06-01    90
## # ℹ 18 more rows

We can group by more than one variable, too.

weather_df |>
  group_by(name, month) |>
  summarize(n_obs = n())
## `summarise()` has grouped output by 'name'. You can override using the
## `.groups` argument.
## # A tibble: 72 × 3
## # Groups:   name [3]
##   name           month      n_obs
##   <chr>          <date>     <int>
## 1 CentralPark_NY 2021-01-01    31
## 2 CentralPark_NY 2021-02-01    28
## 3 CentralPark_NY 2021-03-01    31
## 4 CentralPark_NY 2021-04-01    30
## 5 CentralPark_NY 2021-05-01    31
## 6 CentralPark_NY 2021-06-01    30
## # ℹ 66 more rows

In both cases, the result is a dataframe that includes the grouping variable(s) and the desired summary.

To count things, you could use count() in place of group_by() and summarize() if you remember that this function exists. I’ll also make use of the name argument in count, which defaults to "n".

weather_df |>
  count(month, name = "n_obs")
## # A tibble: 24 × 2
##   month      n_obs
##   <date>     <int>
## 1 2021-01-01    93
## 2 2021-02-01    84
## 3 2021-03-01    93
## 4 2021-04-01    90
## 5 2021-05-01    93
## 6 2021-06-01    90
## # ℹ 18 more rows

count() is a useful tidyverse alternative to Base R’s table function. Both functions produce summaries of how often values appear, but table’s output is of class table and is hard to do any additional work with, while count produces a dataframe you can use or manipulate directly. For an example, run the code below and try to do something useful with the result…

weather_df |>
  pull(month) |> 
  table

You can use summarize() to compute multiple summaries within each group. As an example, we count the number of observations in each month and the number of distinct values of date in each month.

weather_df |>
  group_by(month) |>
  summarize(
    n_obs = n(),
    n_days = n_distinct(date))
## # A tibble: 24 × 3
##   month      n_obs n_days
##   <date>     <int>  <int>
## 1 2021-01-01    93     31
## 2 2021-02-01    84     28
## 3 2021-03-01    93     31
## 4 2021-04-01    90     30
## 5 2021-05-01    93     31
## 6 2021-06-01    90     30
## # ℹ 18 more rows

(2x2 tables)

You might find yourself, someday, wanting to tabulate the frequency of a binary outcome across levels of a binary predictor. In a contrived example, let’s say you want to look at the number of cold and not-cold days in Central Park and Waterhole. We can do this with some extra data manipulation steps and group_by + summarize:

weather_df |> 
  drop_na(tmax) |> 
  mutate(
    cold = case_when(
      tmax <  5 ~ "cold",
      tmax >= 5 ~ "not_cold",
      TRUE      ~ ""
  )) |> 
  filter(name != "Molokai_HI") |> 
  group_by(name, cold) |> 
  summarize(count = n())
## `summarise()` has grouped output by 'name'. You can override using the
## `.groups` argument.
## # A tibble: 4 × 3
## # Groups:   name [2]
##   name           cold     count
##   <chr>          <chr>    <int>
## 1 CentralPark_NY cold        96
## 2 CentralPark_NY not_cold   634
## 3 Waterhole_WA   cold       319
## 4 Waterhole_WA   not_cold   395

This is a “tidy” table, and it’s also a data frame. You could re-organize into a more standard (non-tidy) 2x2 table using pivot_wider, or you could use janitor::tabyl:

weather_df |> 
  drop_na(tmax) |> 
  mutate(cold = case_when(
    tmax <  5 ~ "cold",
    tmax >= 5 ~ "not_cold",
    TRUE     ~ ""
  )) |> 
  filter(name != "Molokai_HI") |> 
  janitor::tabyl(name, cold)
##            name cold not_cold
##  CentralPark_NY   96      634
##    Waterhole_WA  319      395

This isn’t tidy, but it is still a data frame – and that’s noticeably better than usual output from R’s built-in table function. janitor has a lot of little functions like this that turn out to be useful, so when you have some time you might read through all the things you can do. I don’t really love that this is called tabyl, but you can’t always get what you want in life.

(Since we’re on the subject, I think 2x2 tables are kind of silly. When are you ever going to actually analyze data in that format?? In grad school I thought I’d be computing odds ratios by hand everyday (\(OR = AD / BC\), right?!), but really I do that as often as I write in cursive – which is never. Just do a logistic regression adjusting for confounders – because there are always confounders. And is a 2x2 table really that much better than the “tidy” version? There are 4 numbers. )

General summaries

Standard statistical summaries are regularly computed in summarize() using functions like mean(), median(), var(), sd(), mad(), IQR(), min(), and max(). To use these, you indicate the variable to which they apply and include any additional arguments as necessary.

weather_df |>
  group_by(month) |>
  summarize(
    mean_tmax = mean(tmax, na.rm = TRUE),
    mean_prec = mean(prcp, na.rm = TRUE),
    median_tmax = median(tmax),
    sd_tmax = sd(tmax))
## # A tibble: 24 × 5
##   month      mean_tmax mean_prec median_tmax sd_tmax
##   <date>         <dbl>     <dbl>       <dbl>   <dbl>
## 1 2021-01-01     10.9       39.5         5     12.2 
## 2 2021-02-01      9.82      42.6         2.8   12.2 
## 3 2021-03-01     13.7       55.5        NA     NA   
## 4 2021-04-01     16.8       14.7        18.0    9.29
## 5 2021-05-01     19.6       17.3        22.2    9.40
## 6 2021-06-01     24.3       14.1        28.3    8.28
## # ℹ 18 more rows

You can group by more than one variable.

weather_df |>
  group_by(name, month) |>
  summarize(
    mean_tmax = mean(tmax),
    median_tmax = median(tmax))
## `summarise()` has grouped output by 'name'. You can override using the
## `.groups` argument.
## # A tibble: 72 × 4
## # Groups:   name [3]
##   name           month      mean_tmax median_tmax
##   <chr>          <date>         <dbl>       <dbl>
## 1 CentralPark_NY 2021-01-01      4.27         5  
## 2 CentralPark_NY 2021-02-01      3.87         2.8
## 3 CentralPark_NY 2021-03-01     12.3         12.2
## 4 CentralPark_NY 2021-04-01     17.6         18.0
## 5 CentralPark_NY 2021-05-01     22.1         22.2
## 6 CentralPark_NY 2021-06-01     28.1         27.8
## # ℹ 66 more rows

If you want to summarize multiple columns using the same summary, the across function is helpful.

weather_df |>
  group_by(name, month) |>
  summarize(across(tmin:prcp, mean))
## `summarise()` has grouped output by 'name'. You can override using the
## `.groups` argument.
## # A tibble: 72 × 5
## # Groups:   name [3]
##   name           month       tmin  tmax  prcp
##   <chr>          <date>     <dbl> <dbl> <dbl>
## 1 CentralPark_NY 2021-01-01 -1.15  4.27  18.9
## 2 CentralPark_NY 2021-02-01 -1.39  3.87  46.6
## 3 CentralPark_NY 2021-03-01  3.1  12.3   28.0
## 4 CentralPark_NY 2021-04-01  7.48 17.6   22.8
## 5 CentralPark_NY 2021-05-01 12.2  22.1   35.7
## 6 CentralPark_NY 2021-06-01 18.9  28.1   22.2
## # ℹ 66 more rows

The fact that summarize() produces a dataframe is important (and consistent with other functions in the tidyverse). You can incorporate grouping and summarizing within broader analysis pipelines. For example, we can take create a plot based on the monthly summary:

weather_df |>
  group_by(name, month) |>
  summarize(mean_tmax = mean(tmax, na.rm = TRUE)) |>
  ggplot(aes(x = month, y = mean_tmax, color = name)) + 
    geom_point() + geom_line() + 
    theme(legend.position = "bottom")
## `summarise()` has grouped output by 'name'. You can override using the
## `.groups` argument.

The results of group_by() and summarize() are generally tidy, but presenting reader-friendly results for this kind of exploratory analysis often benefits from some un-tidying. For example, the table below shows month-by-month average max temperatures in a more human-readable format.

weather_df |>
  group_by(name, month) |>
  summarize(mean_tmax = mean(tmax, na.rm = TRUE)) |> 
  pivot_wider(
    names_from = name,
    values_from = mean_tmax) |> 
  knitr::kable(digits = 1)
## `summarise()` has grouped output by 'name'. You can override using the
## `.groups` argument.
month CentralPark_NY Molokai_HI Waterhole_WA
2021-01-01 4.3 27.6 0.8
2021-02-01 3.9 26.4 -0.8
2021-03-01 12.3 25.9 2.6
2021-04-01 17.6 26.6 6.1
2021-05-01 22.1 28.6 8.2
2021-06-01 28.1 29.6 15.3
2021-07-01 28.4 30.0 17.3
2021-08-01 28.8 29.5 17.2
2021-09-01 24.8 29.7 12.6
2021-10-01 19.9 29.1 5.5
2021-11-01 11.5 28.8 3.5
2021-12-01 9.6 26.2 -2.1
2022-01-01 2.9 26.6 3.6
2022-02-01 7.7 26.8 3.0
2022-03-01 12.0 27.7 3.4
2022-04-01 15.8 27.7 2.5
2022-05-01 22.3 28.3 5.8
2022-06-01 26.1 29.2 11.1
2022-07-01 30.7 29.5 15.9
2022-08-01 30.5 30.7 18.8
2022-09-01 24.9 30.4 15.2
2022-10-01 17.4 29.2 11.9
2022-11-01 14.0 28.0 2.1
2022-12-01 6.8 27.3 -0.5

Grouped mutate

Summarizing collapses groups into single data points. In contrast, using mutate() in conjuntion with group_by() will retain all original data points and add new variables computed within groups.

Suppose you want to compare the daily max temperature to the annual average max temperature for each station separately, and to plot the result. You could do so using:

weather_df |>
  group_by(name) |>
  mutate(
    mean_tmax = mean(tmax, na.rm = TRUE),
    centered_tmax = tmax - mean_tmax) |> 
  ggplot(aes(x = date, y = centered_tmax, color = name)) + 
    geom_point() 
## Warning: Removed 17 rows containing missing values (`geom_point()`).

Window functions

The previous example used mean() to compute the mean within each group, which was then subtracted from the observed max tempurature. mean() takes n inputs and produces a single output.

Window functions, in contrast, take n inputs and return n outputs, and the outputs depend on all the inputs. There are several categories of window functions; you’re most likely to need ranking functions and offsets, which we illustrate below.

First, we can find the max temperature ranking within month.

weather_df |>
  group_by(name, month) |>
  mutate(temp_ranking = min_rank(tmax))
## # A tibble: 2,190 × 8
## # Groups:   name, month [72]
##   name           id         date        prcp  tmax  tmin month      temp_ranking
##   <chr>          <chr>      <date>     <dbl> <dbl> <dbl> <date>            <int>
## 1 CentralPark_NY USW000947… 2021-01-01   157   4.4   0.6 2021-01-01           14
## 2 CentralPark_NY USW000947… 2021-01-02    13  10.6   2.2 2021-01-01           31
## 3 CentralPark_NY USW000947… 2021-01-03    56   3.3   1.1 2021-01-01           13
## 4 CentralPark_NY USW000947… 2021-01-04     5   6.1   1.7 2021-01-01           20
## 5 CentralPark_NY USW000947… 2021-01-05     0   5.6   2.2 2021-01-01           19
## 6 CentralPark_NY USW000947… 2021-01-06     0   5     1.1 2021-01-01           16
## # ℹ 2,184 more rows

This sort of ranking is useful when filtering data based on rank. We could, for example, keep only the day with the lowest max temperature within each month:

weather_df |>
  group_by(name, month) |>
  filter(min_rank(tmax) < 2)
## # A tibble: 92 × 7
## # Groups:   name, month [72]
##   name           id          date        prcp  tmax  tmin month     
##   <chr>          <chr>       <date>     <dbl> <dbl> <dbl> <date>    
## 1 CentralPark_NY USW00094728 2021-01-29     0  -3.8  -9.9 2021-01-01
## 2 CentralPark_NY USW00094728 2021-02-08     0  -1.6  -8.2 2021-02-01
## 3 CentralPark_NY USW00094728 2021-03-02     0   0.6  -6   2021-03-01
## 4 CentralPark_NY USW00094728 2021-04-02     0   3.9  -2.1 2021-04-01
## 5 CentralPark_NY USW00094728 2021-05-29   117  10.6   8.3 2021-05-01
## 6 CentralPark_NY USW00094728 2021-05-30   226  10.6   8.3 2021-05-01
## # ℹ 86 more rows

We could also keep the three days with the highest max temperature:

weather_df |>
  group_by(name, month) |>
  filter(min_rank(desc(tmax)) < 4)
## # A tibble: 269 × 7
## # Groups:   name, month [72]
##   name           id          date        prcp  tmax  tmin month     
##   <chr>          <chr>       <date>     <dbl> <dbl> <dbl> <date>    
## 1 CentralPark_NY USW00094728 2021-01-02    13  10.6   2.2 2021-01-01
## 2 CentralPark_NY USW00094728 2021-01-14     0   9.4   3.9 2021-01-01
## 3 CentralPark_NY USW00094728 2021-01-16   198   8.3   2.8 2021-01-01
## 4 CentralPark_NY USW00094728 2021-02-16   208  10.6   1.1 2021-02-01
## 5 CentralPark_NY USW00094728 2021-02-24     0  12.2   3.9 2021-02-01
## 6 CentralPark_NY USW00094728 2021-02-25     0  10     4.4 2021-02-01
## # ℹ 263 more rows

In both of these, we’ve skipped a mutate() statement that would create a ranking variable, and gone straight to filtering based on the result.

Offsets, especially lags, are used to compare an observation to it’s previous value. This is useful, for example, to find the day-by-day change in max temperature within each station over the year:

weather_df |>
  group_by(name) |>
  mutate(temp_change = tmax - lag(tmax))
## # A tibble: 2,190 × 8
## # Groups:   name [3]
##   name           id          date        prcp  tmax  tmin month      temp_change
##   <chr>          <chr>       <date>     <dbl> <dbl> <dbl> <date>           <dbl>
## 1 CentralPark_NY USW00094728 2021-01-01   157   4.4   0.6 2021-01-01      NA    
## 2 CentralPark_NY USW00094728 2021-01-02    13  10.6   2.2 2021-01-01       6.2  
## 3 CentralPark_NY USW00094728 2021-01-03    56   3.3   1.1 2021-01-01      -7.3  
## 4 CentralPark_NY USW00094728 2021-01-04     5   6.1   1.7 2021-01-01       2.8  
## 5 CentralPark_NY USW00094728 2021-01-05     0   5.6   2.2 2021-01-01      -0.5  
## 6 CentralPark_NY USW00094728 2021-01-06     0   5     1.1 2021-01-01      -0.600
## # ℹ 2,184 more rows

This kind of variable might be used to quantify the day-by-day variability in max temperature, or to identify the largest one-day increase:

weather_df |>
  group_by(name) |>
  mutate(temp_change = tmax - lag(tmax)) |>
  summarize(
    temp_change_sd = sd(temp_change, na.rm = TRUE),
    temp_change_max = max(temp_change, na.rm = TRUE))
## # A tibble: 3 × 3
##   name           temp_change_sd temp_change_max
##   <chr>                   <dbl>           <dbl>
## 1 CentralPark_NY           4.43            12.2
## 2 Molokai_HI               1.24             5.6
## 3 Waterhole_WA             3.04            11.1

Limitations

summarize() can only be used with functions that return a single-number summary. This creates a ceiling, even if it is very high. Later we’ll see how to aggregate data in a more general way, and how to perform complex operations on the resulting sub-datasets.

Revisiting examples

We’ve seen the PULSE and FAS datasets on several occasions, and we’ll briefly revisit them here.

Learning Assessment: In the PULSE data, the primary outcome is BDI score; it’s observed over follow-up visits, and we might ask if the typical BDI score values are roughly similar at each. Try to write a code chunk that imports, cleans, and summarizes the PULSE data to examine the mean and median at each visit. Export the results of this in a reader-friendly format.

Solution

The code chunk below imports and tidies the PUSLE data, produces the desired information, and exports it using knitr::kable.

pulse_data = 
  haven::read_sas("./data/public_pulse_data.sas7bdat") |>
  janitor::clean_names() |>
  pivot_longer(
    bdi_score_bl:bdi_score_12m,
    names_to = "visit", 
    names_prefix = "bdi_score_",
    values_to = "bdi") |>
  select(id, visit, everything()) |>
  mutate(
    visit = replace(visit, visit == "bl", "00m"),
    visit = factor(visit, levels = str_c(c("00", "01", "06", "12"), "m"))) |>
  arrange(id, visit)

pulse_data |> 
  group_by(visit) |> 
  summarize(
    mean_bdi = mean(bdi, na.rm = TRUE),
    median_bdi = median(bdi, na.rm = TRUE)) |> 
  knitr::kable(digits = 3)
This quick summary suggests a relatively large drop in the typical BDI score from baseline to 1 month, with small or no changes thereafter.

Learning Assessment: In the FAS data, there are several outcomes of interest; for now, focus on post-natal day on which a pup is able to pivot. Two predictors of interest are the dose level and the day of treatment. Produce a reader-friendly table that quantifies the possible associations between dose, day of treatment, and the ability to pivot.

Solution

The code chunk below imports the litters and pups data, joins them, produces the desired information, un-tidies the result, and exports a table using knitr::kable.

pup_data = 
  read_csv("./data/FAS_pups.csv") |>
  janitor::clean_names() |>
  mutate(sex = recode(sex, `1` = "male", `2` = "female")) 

litter_data = 
  read_csv("./data/FAS_litters.csv") |>
  janitor::clean_names() |>
  separate(group, into = c("dose", "day_of_tx"), sep = 3)

fas_data = left_join(pup_data, litter_data, by = "litter_number") 

fas_data |> 
  group_by(dose, day_of_tx) |> 
  drop_na(dose) |> 
  summarize(mean_pivot = mean(pd_pivot, na.rm = TRUE)) |> 
  pivot_wider(
    names_from = dose, 
    values_from = mean_pivot) |> 
  knitr::kable(digits = 3)

These results may suggest that pups in the control group are able to pivot earlier than pups in the low-dose group, but it is unclear if there are differences between the control and moderate-dose groups or if day of treatment is an important predictor.

Note: In both of these examples, the data are structure such that repeated observations are made on the same study units. In the PULSE data, repeated observations are made on subjects over time; in the FAS data, pups are “repeated observations” within litters. The analyses here, and plots made previously, are exploratory – any more substantial claims would require appropriate statistical analysis for non-independent samples.

Other materials

The code that I produced working examples in lecture is here.